Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)
Ref | Expression | ||
---|---|---|---|
Hypothesis | necon2bi.1 | ⊢ ( 𝜑 → 𝐴 ≠ 𝐵 ) | |
Assertion | necon2bi | ⊢ ( 𝐴 = 𝐵 → ¬ 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon2bi.1 | ⊢ ( 𝜑 → 𝐴 ≠ 𝐵 ) | |
2 | 1 | neneqd | ⊢ ( 𝜑 → ¬ 𝐴 = 𝐵 ) |
3 | 2 | con2i | ⊢ ( 𝐴 = 𝐵 → ¬ 𝜑 ) |